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%I #4 Dec 15 2017 16:29:42
%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,3,3,1,1,1,1,4,5,4,1,1,1,1,5,7,7,5,
%T 1,1,1,1,7,10,11,10,7,1,1,1,1,10,17,18,18,17,10,1,1,1,1,14,28,34,32,
%U 34,28,14,1,1,1,1,19,43,59,62,62,59,43,19,1,1,1,1,26,66,100,118,148,118,100,66,26
%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s.
%C Table starts
%C .1.1..1..1...1...1...1....1....1.....1.....1......1......1.......1.......1
%C .1.1..1..1...1...1...1....1....1.....1.....1......1......1.......1.......1
%C .1.1..2..3...4...5...7...10...14....19....26.....36.....50......69......95
%C .1.1..3..5...7..10..17...28...43....66...105....168....264.....413.....651
%C .1.1..4..7..11..18..34...59..100...174...309....538....930....1620....2835
%C .1.1..5.10..18..32..62..118..227...439...839...1592...3037....5823...11144
%C .1.1..7.17..34..62.148..347..786..1702..3761...8400..18843...41959...93233
%C .1.1.10.28..59.118.347..960.2418..5862.15035..39090.100159..253642..646112
%C .1.1.14.43.100.227.786.2418.6802.18758.55226.162010.467274.1341081.3887275
%H R. H. Hardin, <a href="/A296554/b296554.txt">Table of n, a(n) for n = 1..449</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1)
%F k=3: a(n) = a(n-1) +a(n-4)
%F k=4: a(n) = a(n-1) +2*a(n-4) +a(n-7)
%F k=5: a(n) = a(n-1) +3*a(n-4) +a(n-6) +3*a(n-7) +a(n-10)
%F k=6: a(n) = a(n-1) +4*a(n-4) +a(n-5) +3*a(n-6) +6*a(n-7) +2*a(n-9) +4*a(n-10) +a(n-13)
%e Some solutions for n=7 k=4
%e ..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1
%e ..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..1..1..0. .0..1..1..1
%e ..0..0..0..0. .0..1..1..0. .0..0..0..0. .1..1..1..0. .0..1..1..0
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0
%e ..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..1..1..0
%e ..1..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..1. .1..1..1..0
%e ..1..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..1..0. .1..1..0..0
%Y Column 3 is A003269(n+2).
%K nonn,tabl
%O 1,13
%A _R. H. Hardin_, Dec 15 2017
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